TuningGoal.Gain class

Description

Use the TuningGoal.Gain object to specify a
constraint that limits the gain from a specified input to a specified
output. Use this requirement for control system tuning with tuning
commands such as systune or looptune.

When you use a TuningGoal.Gain requirement,
the software attempts to tune the system so that the gain from the
specified input to the specified output does not exceed the specified
value. By default, the constraint is applied with the loop closed.
To apply the constraint to an open-loop response, use the Openings property
of the TuningGoal.Gain object.

You can use a gain constraint to:

Enforce a design requirement of disturbance rejection
across a particular input/output pair, by constraining the gain to
be less than 1

Enforce a custom roll-off rate in a particular frequency
band, by specifying a gain profile in that band

Construction

Req =
TuningGoal.Gain(inputname,outputname,gainvalue) creates
a tuning requirement Req. This requirement constrains
the gain from inputname to outputname to
remain below the value gainvalue.

You can specify the inputname or outputname as
cell arrays (vector-valued signals). If you do so, then the tuning
requirement constrains the largest singular value of the transfer
matrix from inputname to outputname.
See sigma for more information
about singular values.

Req = TuningGoal.Gain(inputname,outputname,gainprofile) specifies
the maximum gain as a function of frequency. You can specify the target
gain profile (maximum gain across the I/O pair) as a smooth transfer
function. Alternatively, you can sketch a piecewise error profile
using an frd model.

Input Arguments

inputname

Input signals for the requirement, specified as a string or
as a cell array of strings, for multiple-input requirements.

If you are using the requirement to tune a Simulink® model
of a control system, then inputname can include:

Any model input.

Any linear analysis point marked in the model.

Any linear analysis point in an slTuner interface associated with the Simulink model.
Use addPoint to add analysis
points to the slTuner interface. Use getPoints to get the list of analysis
points available in an slTuner interface to your
model.

If you are using the requirement to tune a generalized state-space
(genss) model of a control system, then inputname can
include:

For example, if you are tuning a control system model, T,
then inputname can be a string contained in T.InputName.
Also, if T contains an AnalysisPoint block
with a location named AP_u, then inputname can
include 'AP_u'. Use getPoints to
get a list of analysis points available in a genss model.

If inputname is an AnalysisPoint location
of a generalized model, the input signal for the requirement is the
implied input associated with the AnalysisPoint block:

Output signals for the requirement, specified as a string or
as a cell array of strings, for multiple-output requirements.

If you are using the requirement to tune a Simulink model
of a control system, then outputname can include:

Any model output.

Any linear analysis point marked in the model.

Any linear analysis point in an slTuner interface associated with the Simulink model.
Use addPoint to add analysis
points to the slTuner interface. Use getPoints to get the list of analysis
points available in an slTuner interface to your
model.

If you are using the requirement to tune a generalized state-space
(genss) model of a control system, then outputname can
include:

For example, if you are tuning a control system model, T,
then inputname can be a string contained in T.OutputName.
Also, if T contains an AnalysisPoint block
with a location named AP_y, then inputname can
include 'AP_y'. Use getPoints to
get a list of analysis points available in a genss model.

If outputname is an AnalysisPoint location
of a generalized model, the output signal for the requirement is the
implied output associated with the AnalysisPoint block:

gainvalue is a scalar value. If the signals inputname or outputname are
vector-valued signals, then gainvalue constrains
the largest singular value of the transfer matrix from inputname to outputname.
See sigma for more information
about singular values.

gainprofile

Gain profile as a function of frequency. The gain constraint Req specifies
that the gain from inputname to outputname at
a particular frequency is less than gainprofile.
You can specify gainprofile as a smooth transfer
function (tf , zpk, or ss model).
Alternatively, you can sketch a piecewise gain profile using a frd model or the makeweight function. When you do so,
the software automatically maps the gain profile onto a zpk model.
The magnitude of this zpk model approximates
the desired gain profile. Use viewSpec(Req) to
plot the magnitude of the zpk model.

gainprofile is a SISO transfer function.
If inputname or outputname are
cell arrays, gainprofile applies to all I/O pairs
from inputname to outputname

Properties

MaxGain

Maximum gain as a function of frequency,
expressed as a SISO zpk model.

The software automatically maps the gainvalue or gainprofile input
arguments to a zpk model. The magnitude of this zpk model
approximates the desired gain profile, and is stored in the MaxGain property.
Use viewSpec(Req) to plot the magnitude of MaxGain.

Focus

Frequency band in which tuning requirement is enforced, specified
as a row vector of the form [min,max].

Set the Focus property to limit enforcement
of the requirement to a particular frequency band. Express this value
in the frequency units of the control system model you are tuning
(rad/TimeUnit). For example, suppose Req is
a requirement that you want to apply only between 1 and 100 rad/s.
To restrict the requirement to this band, use the following command:

Req.Focus = [1,100];

Default: [0,Inf] for continuous time; [0,pi/Ts] for
discrete time, where Ts is the model sample time.

By default, TuningGoal.Gain imposes a stability
requirement on the closed-loop transfer function from the specified
inputs to outputs, in addition to the gain requirement. If stability
is not required or cannot be achieved, set Stabilize to false to
remove the stability requirement. For example, if the gain constraint
applies to an unstable open-loop transfer function, set Stabilize to false.

Default: 1(true)

InputScaling

Input signal scaling, specified as a vector of positive real
values.

Use this property to specify the relative amplitude of each
entry in vector-valued input signals when the choice of units results
in a mix of small and large signals. This information is used to scale
the closed-loop transfer function from Input to Output when
the tuning requirement is evaluated.

Suppose T(s) is the closed-loop
transfer function from Input to Output.
The requirement is evaluated for the scaled transfer function Do–1T(s)Di.
The diagonal matrices Do and Di have
the OutputScaling and InputScaling values
on the diagonal, respectively.

The default value, [] , means no scaling.

Default: []

OutputScaling

Output signal scaling, specified as a vector of positive real
values.

Use this property to specify the relative amplitude of each
entry in vector-valued output signals when the choice of units results
in a mix of small and large signals. This information is used to scale
the closed-loop transfer function from Input to Output when
the tuning requirement is evaluated.

Suppose T(s) is the closed-loop
transfer function from Input to Output.
The requirement is evaluated for the scaled transfer function Do–1T(s)Di.
The diagonal matrices Do and Di have
the OutputScaling and InputScaling values
on the diagonal, respectively.

The default value, [] , means no scaling.

Default: []

Input

Input signal names, specified as a cell array of strings. These
strings specify the names of the inputs of the transfer function that
the tuning requirement constrains. The initial value of the Input property
is set by the inputname input argument when you
construct the requirement object.

Output

Output signal names, specified as a cell array of strings. These
strings specify the names of the outputs of the transfer function
that the tuning requirement constrains. The initial value of the Output property
is set by the outputname input argument when
you construct the requirement object.

Models

Models to which the tuning requirement applies, specified as
a vector of indices.

Use the Models property when tuning an array
of control system models with systune, to enforce
a tuning requirement for a subset of models in the array. For example,
suppose you want to apply the tuning requirement, Req,
to the second, third, and fourth models in a model array passed to systune.
To restrict enforcement of the requirement, use the following command:

Req.Models = 2:4;

When Models = NaN, the tuning requirement
applies to all models.

Default: NaN

Openings

Feedback loops to open when evaluating the requirement, specified
as a cell array of strings that identify loop-opening locations. The
tuning requirement is evaluated against the open-loop configuration
created by opening feedback loops at the locations you identify.

If you are using the requirement to tune a Simulink model
of a control system, then Openings can include
any linear analysis point marked in the model, or any linear analysis
point in an slTuner interface
associated with the Simulink model. Use addPoint to add analysis points and
loop openings to the slTuner interface. Use getPoints to get the list of analysis
points available in an slTuner interface to your
model.

If you are using the requirement to tune a generalized state-space
(genss) model of a control system, then Openings can
include any AnalysisPoint location
in the control system model. Use getPoints to
get the list of analysis points available in the genss model.

Default: {}

Name

Name of the requirement object, specified as a string.

For example, if Req is a requirement:

Req.Name = 'LoopReq';

Default: []

Algorithms

When you tune a control system using a TuningGoal object
to specify a tuning requirement, the software converts the requirement
into a normalized scalar value f(x),
where x is the vector of free (tunable) parameters
in the control system. The software then adjusts the parameter values
to minimize f(x) or to drive f(x)
below 1 if the tuning requirement is a hard constraint.

For the TuningGoal.Gain requirement, f(x)
is given by:

f(x)=‖1MaxGainDo−1T(s,x)Di‖∞.

T(s,x)
is the closed-loop transfer function from Input to Output. Do and Di are
diagonal matrices with the OutputScaling and InputScaling property
values on the diagonal, respectively. ‖⋅‖∞ denotes
the H∞ norm (see norm).

Examples

Disturbance rejection

Create a gain constraint that enforces a disturbance rejection
requirement from a signal 'du' to a signal 'u'.

Req = TuningGoal.Gain('du','u',1);

This requirement specifies that the maximum gain of the response
from 'du' to 'u' not exceed
1 (0 dB).

Custom roll-off specification

Create a gain constraint that constrains the response from a signal 'du' to a signal 'u' to roll off at 20 dB/decade at frequencies greater than 1. The gain constraint also specifies disturbance rejection (maximum gain of 1) in the frequency range [0,1].

These commands use a frd model to specify the gain profile as a function of frequency. The maximum gain of 1 dB at the frequency 1 rad/s, together with the maximum gain of 0.01 dB at the frequency 100 rad/s, specifies the desired rolloff of 20 dB/decade.

The software converts gmax into a smooth function of frequency that approximates the piecewise specified requirement. Display the error requirement using viewSpec.

viewSpec(Req)

The yellow region indicates where the requirement is violated.

Disturbance rejection

Create a gain constraint that enforces a disturbance rejection
requirement from a signal 'du' to a signal 'u'.

Req = TuningGoal.Gain('du','u',1);

This requirement specifies that the maximum gain of the response
from 'du' to 'u' not exceed
1 (0 dB).